Question #4a0d0399 - SAT Suite Question Bank

ID: 4a0d0399

Modded SAT Question Bank by Abdullah Mallik

The function $f$ is defined by $f (x) = a^{x} + b$ , where $a$ and $b$ are constants. In the $x y$ -plane, the graph of $y = f (x)$ has an $x$ -intercept at $left parenthesis 2 comma 0 right parenthesis$ and a $y$ -intercept at $left parenthesis 0 comma negative 323 right parenthesis$ . What is the value of $b$ ?

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Correct Answer: -324

Rationale

The correct answer is $negative 324$ . It's given that the function $f$ is defined by $f (x) = a^{x} + b$ , where $a$ and $b$ are constants. It's also given that the graph of $y = f (x)$ has a y-intercept at $left parenthesis 0 comma negative 323 right parenthesis$ . It follows that $f (0) = - 323$ . Substituting $0$ for $x$ and $negative 323$ for $f (x)$ in $f (x) = a^{x} + b$ yields $- 323 = a^{0} + b$ , or $- 323 = 1 + b$ . Subtracting $1$ from each side of this equation yields $- 324 = b$ . Therefore, the value of $b$ is $negative 324$ .

Question Difficulty: Hard